Global ordinals is a data-structure on top of doc values, that maintains an
incremental numbering for each unique term in a lexicographic order. Each
term has a unique number and the number of term A is lower than the
number of term B. Global ordinals are only supported with
keyword and text fields. In keyword fields, they
are available by default but text fields can only use them when fielddata,
with all of its associated baggage, is enabled.

Doc values (and fielddata) also have ordinals, which is a unique numbering for
all terms in a particular segment and field. Global ordinals just build on top
of this, by providing a mapping between the segment ordinals and the global
ordinals, the latter being unique across the entire shard. Given that global
ordinals for a specific field are tied to all the segments of a shard, they
need to be entirely rebuilt whenever a once new segment becomes visible.

Global ordinals are used for features that use segment ordinals, such as
the terms aggregation,
to improve the execution time. A terms aggregation relies purely on global
ordinals to perform the aggregation at the shard level, then converts global
ordinals to the real term only for the final reduce phase, which combines
results from different shards.

The loading time of global ordinals depends on the number of terms in a field,
but in general it is low, since it source field data has already been loaded.
The memory overhead of global ordinals is a small because it is very
efficiently compressed.

By default, global ordinals are loaded at search-time, which is the right
trade-off if you are optimizing for indexing speed. However, if you are more
interested in search speed, it could be interesting to set
eager_global_ordinals: true on fields that you plan to use in terms
aggregations: